Groundwater levels in cold climates respond to recharge that is delayed by snow accumulation and melt, which makes data-driven modelling more difficult than in rain-dominated regions. This study models monthly groundwater levels (GWL) of an observation well near Heby, Sweden (1981–2020), using precipitation, potential evaporation and temperature from the E-OBS dataset. A degree-day snow routine was used to convert precipitation into rain and snowmelt, and the resulting effective water input was used as the main predictor. Multiple linear regression (MLR), support vector regression (SVR), random forest (RF), long short-term memory (LSTM) and two hybrid models in which SVR was tuned by the sparrow search algorithm (SVR-SSA) and particle swarm optimization (SVR-PSO) were evaluated in two scenarios: simulation from meteorological inputs only (S1) and one-month-ahead forecasting with lagged GWL (S2). The models were trained on 1981–2008, validated on 2009–2013 and tested on 2014–2020. In S1 the LSTM clearly outperformed all other models (test RMSE = 12.5 cm, NSE = 0.68), while the hybrid SVRs (NSE = 0.45) generalized worse than the default SVR (NSE = 0.64) despite lower validation errors. In S2 SVR-SSA was the best model (RMSE = 7.6 cm, NSE = 0.88), improving on persistence (RMSE = 11.0 cm) by 30%. The six-month cumulative effective water input was the most important meteorological predictor. The results show that sequence learning is most valuable when no past groundwater observations are available, and that metaheuristic tuning is beneficial mainly in the autoregressive forecasting setting.